We now discuss further possible generalizations. First, we expect that \( \operatorname{div}A \in L^N(\Omega )\)  could be avoided. In fact, this assumption is used only to trigger the \(\alpha _0\) -Hölder estimates, which were obtained for equations in divergence form. Indeed, \( \operatorname{div}A \in L^N(\Omega )\)  is needed when transforming (REF ) into a divergence form equation. We believe that \(\alpha _0\) -Hölder estimates could be obtained directly for (REF ), and for merely continuous \(A\) . Note that this question is related with the \(L^q\) -maximal regularity in the critical case \(q = q_0\) . Despite a statement as in Theorem REF  cannot hold (again by (REF ) it is possible to construct a sequence of \(u_n, f_n\)  solving (REF ) such that \(u_n \rightarrow \infty \)  in \(W^{2,q_0}\)  while \(f_n\)  remains bounded in \(L^{q_0}\) , see e.g. [1]}), it should be possible to control \(u\)  in \(W^{2,q_0}\)  whenever \(f\)  lies in a set of \(L^{q_0}\)  uniformly integrable functions. This has been shown to hold for subquadratic (\(\gamma < 2\) ) problems [2]}.
